%0 Journal Article
	%A Aziz Sezgin
	%D 2015
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 104, 2015
	%T A Boundary Backstepping Control Design for 2-D, 3-D and N-D Heat Equation
	%U https://publications.waset.org/pdf/10002727
	%V 104
	%X We consider the problem of stabilization of an unstable
heat equation in a 2-D, 3-D and generally n-D domain by deriving a
generalized backstepping boundary control design methodology. To
stabilize the systems, we design boundary backstepping controllers
inspired by the 1-D unstable heat equation stabilization procedure.
We assume that one side of the boundary is hinged and the other
side is controlled for each direction of the domain. Thus, controllers
act on two boundaries for 2-D domain, three boundaries for 3-D
domain and ”n” boundaries for n-D domain. The main idea of the
design is to derive ”n” controllers for each of the dimensions by
using ”n” kernel functions. Thus, we obtain ”n” controllers for the
”n” dimensional case. We use a transformation to change the system
into an exponentially stable ”n” dimensional heat equation. The
transformation used in this paper is a generalized Volterra/Fredholm
type with ”n” kernel functions for n-D domain instead of the one
kernel function of 1-D design.
	%P 499 - 504